Calculate rhombus area, perimeter, side length, diagonals, altitude, and inradius with step-by-step geometric solutions.
Did this calculation save you time?
Student ProjectHi! I'm a student developer building Calculat in my spare time. I was tired of searching for basic math tools and having to click through 10 spammy popups, loan ads, and cookie trackers.
I keep this website 100% free, private, and ad-free. If this helped you with your homework, project, or finances today, bookmarking this page or telling a friend helps me keep building more free tools!
A rhombus is a quadrilateral whose four sides all have equal length. Opposite sides are parallel, and diagonals intersect perpendicularly (at 90°) while bisecting each other.
A = \frac{1}{2}d_1 d_2, \quad s = \sqrt{\left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2}, \quad P = 4sArea is half the product of the two perpendicular diagonals. Side length is found via right triangles formed by the intersecting semi-diagonals.
Scenario: Find area and perimeter for diagonals d₁ = 12 and d₂ = 16
Area: A = ½ × 12 × 16 = 96
Semi-diagonals: 12/2 = 6, 16/2 = 8
Side length: s = √(6² + 8²) = √(36 + 64) = √100 = 10
Perimeter: P = 4 × 10 = 40
The diagonals divide the rhombus into four congruent right triangles. Summing their areas yields ½ × d₁ × d₂.
Yes, opposite angles of a rhombus are equal, and adjacent angles are supplementary (they sum to 180°).
Yes, Area = s² × sin(θ), where θ is any interior angle.
The inradius is r = (d₁ × d₂) / (4s) = h / 2, representing the radius of the inscribed circle.
Calculate parallelogram area, perimeter, base, height, and side lengths with step-by-step geometric formulas.
Calculate square area, perimeter, diagonal, inradius, and circumradius from side length with step-by-step formulas.
Calculate trapezium (trapezoid) area, perimeter, mid-segment (median), bases, and height with step-by-step mathematical steps.